Ordering Numbers and Decimals
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ISEE Lower Level: Mathematics Achievement › Ordering Numbers and Decimals
A scientist recorded a temperature of 23.67 degrees Celsius. The next reading must be between 23.67 and 23.7 degrees Celsius. Which of the following could be the next reading?
23.71 degrees
23.068 degrees
23.68 degrees
23.669 degrees
Explanation
The question asks for a number that is greater than 23.67 and less than 23.7. To compare easily, we can write 23.7 as 23.70. We are looking for a number between 23.67 and 23.70. The number 23.68 is greater than 23.67 and less than 23.70, so it is a possible value.
A scientist is trying to create a solution with a temperature of exactly 25 degrees Celsius. She records four attempts: 25.01 degrees, 24.9 degrees, 25.11 degrees, and 24.995 degrees. Which temperature is closest to 25 degrees?
25.01 degrees
24.9 degrees
24.995 degrees
25.11 degrees
Explanation
To find which temperature is closest to 25 degrees, we must calculate the difference between each attempt and 25. The differences are: |25.01 - 25| = 0.01; |24.9 - 25| = 0.1; |25.11 - 25| = 0.11; |24.995 - 25| = 0.005. The smallest difference is 0.005, which corresponds to the temperature 24.995 degrees.
Using the digits 4, 1, 8, and 5 exactly once, what is the smallest possible number that can be created that is greater than 40?
14.58
41.58
41.85
45.18
Explanation
The number must be greater than 40, so the tens digit must be 4 or larger. To make the number as small as possible, we should choose the smallest possible digit for the tens place, which is 4. For the ones place, we should choose the smallest remaining digit, which is 1. For the decimal part, we should arrange the remaining digits (5 and 8) from smallest to largest. So, the tenths digit is 5 and the hundredths digit is 8. The resulting number is 41.58.
A certain number has a 7 in the tenths place. The number is greater than 15.68 and less than 15.8. Which of the following could be the number?
15.67
15.75
15.87
16.7
Explanation
The number must satisfy three conditions: 1) have a 7 in the tenths place, 2) be greater than 15.68, and 3) be less than 15.8. Let's check the choices. A) 15.67 fails conditions 1 and 2. C) 15.87 fails condition 3. D) 16.7 fails condition 3. B) 15.75 has a 7 in the tenths place, is greater than 15.68, and is less than 15.8. It satisfies all conditions.
Four friends measured the lengths of their pet snakes. Leo's snake is 1.45 meters, Mia's is 1.5 meters, Noah's is 1.405 meters, and Ava's is 1.05 meters. Which list shows the snakes in order from shortest to longest?
Ava, Noah, Mia, Leo
Ava, Noah, Leo, Mia
Mia, Leo, Noah, Ava
Ava, Leo, Noah, Mia
Explanation
To compare the lengths, it is helpful to write them with the same number of decimal places by adding trailing zeros. The lengths are: Leo (1.450 m), Mia (1.500 m), Noah (1.405 m), and Ava (1.050 m). Ordering these decimal numbers from least (shortest) to greatest (longest) gives: 1.050, 1.405, 1.450, 1.500. This corresponds to the order: Ava, Noah, Leo, Mia.
Sam is writing a list of numbers in increasing order: 10.08, 10.1, _____, 10.11. Which of the following numbers could be placed in the blank to keep the list in order?
10.09
10.101
10.111
10.2
Explanation
The missing number must be greater than 10.1 and less than 10.11. To make comparison easier, we can add zeros to give them the same number of decimal places: the number must be between 10.100 and 10.110. Let's check the options. A) 10.09 is less than 10.1. C) 10.2 is greater than 10.11. D) 10.111 is greater than 10.11. B) 10.101 is greater than 10.100 and less than 10.110, so it fits in the blank.
Which of the following numbers, written in expanded form, represents the greatest value?
(8 x 100) + (2 x 10) + (9 x 1) + (9 x 0.1)
(8 x 100) + (3 x 10) + (5 x 1) + (2 x 0.01)
(8 x 100) + (3 x 10) + (5 x 1) + (1 x 0.1) + (9 x 0.01)
(8 x 100) + (3 x 10) + (4 x 1) + (9 x 0.1)
Explanation
First, convert each number from expanded form to standard form. A) 835.02. B) 834.9. C) 835.19. D) 829.9. Now, compare these four numbers. D is the smallest because its tens digit is 2. B is the next smallest because its ones digit is 4. Comparing A (835.02) and C (835.19), we see that C is greater because its tenths digit (1) is greater than A's tenths digit (0). Therefore, 835.19 is the greatest value.
A bookshelf contains four books with the following weights: Book A is 2 pounds, Book B is 1.85 pounds, Book C is 2.1 pounds, and Book D is 1.9 pounds. Which is the third heaviest book?
Book C
Book B
Book D
Book A
Explanation
To find the third heaviest book, we must first list the weights in order from heaviest (greatest) to lightest (least). The weights are 2.1, 2.0, 1.9, and 1.85 pounds. The list of books from heaviest to lightest is: Book C (2.1 lbs), Book A (2.0 lbs), Book D (1.9 lbs), and Book B (1.85 lbs). The third book in this ordered list is Book D.
In a pie-eating contest, the winner is the person who consumes the greatest weight of pie. Jamal ate 3.8 pounds, Kelly ate 3.75 pounds, Ben ate 3.805 pounds, and Maria ate 3.57 pounds. Who won the silver medal, which is awarded for second place?
Kelly
Jamal
Maria
Ben
Explanation
To find the second-place winner, we must order the weights from greatest to least. Let's align the decimal places: Ben (3.805), Jamal (3.800), Kelly (3.750), Maria (3.570). The greatest weight is 3.805 pounds, so Ben finished in first place. The second-greatest weight is 3.8 pounds, so Jamal finished in second place.
The acceptable weight for a package at a certain post office is between 5.08 kilograms and 5.8 kilograms, inclusive. This means the weight can be equal to 5.08 kg or 5.8 kg. Which of the following package weights is NOT acceptable?
5.1 kg
5.079 kg
5.79 kg
5.80 kg
Explanation
An acceptable weight must be greater than or equal to 5.08 kg and less than or equal to 5.8 kg. Let's check each option. A) 5.80 kg is equal to 5.8 kg, so it is acceptable. B) 5.1 kg is greater than 5.08 kg and less than 5.8 kg, so it is acceptable. C) 5.079 kg is less than 5.08 kg, so it is NOT acceptable. D) 5.79 kg is greater than 5.08 kg and less than 5.8 kg, so it is acceptable.